Another Joiner

A joiner had two pieces of wood of the shapes and relative proportions shown in the diagram. 
He wished to cut them into as few pieces as possible so that they could be fitted together, without waste, to form a perfectly square table-top. 

How should he have done it? 

There is no necessity to give measurements, for if the smaller piece (which is half a square) be made a little too large or a little too small it will not affect the method of solution.

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Math Genius